The emphasis in the seminar is on discussion & understanding of current literature.

Overview:

[DiV] Oct. 21 I will begin with a discussion of equations of motion and Hamiltonians for circuits. There are three basic papers, Devoret, "BKD", and Burkard; I will follow Burkard almost completely. I will concentrate on the theme of "singular perturbations", i.e., the fact that adding a very small additional element (e.g., capacitor, inductor) can completely change our description of the system. I will illustrate this with the problem of the DC SQUID with an additional inductance, and the transmon with additional "parasitic" elements. An exercise will be given (see Oct. 28). Here are lecture notes.

[DiV] Oct. 28 Students will present an analysis, based on the ideas of Mooij, of the flux qubit with and without a loop inductance. Here are lecture notes.

[DiV] Nov. 18 We will save further study of the Brooks, Preskill, Kitaev qubit to later in the semester. Today we will see how circuit models can be derived from physical models of electrical structures. The "black box" approach of Nigg et al. is explained, put in the context of the general theory of electric response; we will learn about "positive real" responses (from the book by Newcomb 'Linear Multiport Synthesis', Chapters 3 and 4), the limitations of "lossy Foster synthesis" (see Montgomery et al., p. 216), and derive the general Brune representation of electric response (see selection from E. Guillemin, Synthesis of Passive Networks ). Another good source for network theory is Carlin. Here are the lecture notes.